A plane tiling generates a dynamical system `$(X,\mathbb{R}^2)$`

, where `$X$`

is the closure (w.r.t. a certain topology) of the orbit of the tiling under the actions of `$\mathbb{R}^2$`

. This `$X$`

is called the hull of the tiling.
For more details, see for instance [Kel00]
and references therein.

[Kel00]

Kellendonk, J, Putnam, I

**Tilings, $C^{*}$-algebras and K-theory**

*Directions in mathematical quasicrystals*
CRM Monogr. Ser., 13, Amer. Math. Soc., Providence, RI, 2000. ,
177–206,
MR1798993